As radio communication systems, for example, conventionally there are known multi-carrier modulation systems represented by OFDM (Orthogonal Frequency Division Multiplexing) system and DMT (Discrete Multitone) system. These systems are employed in wireless LANs, ADSLs, and the like. These multi-carrier modulation systems insert carries, which are orthogonal, in a plurality of frequencies, and transmit the carriers. These systems are characterized by having, for example, a guard interval or a cyclic prefix as a function for removing an influence of delayed waves caused by a propagation path or the like between a transmitter and a receiver. The receiver applies FFT to an OFDM symbol, from which the guard interval has been removed, to remove influences of delayed waves in the guard interval and correctly demodulate data.
However, in the OFDM system, intersymbol interference occurs and characteristics are substantially deteriorated if delayed waves that continue even after (i.e., exceed) the guard interval arrive. This problem can be overcome by adding a guard interval longer than the presumed delay time. However, in this approach, an overhead of the guard interval increases which leads to lower transmission efficiency.
As another approach to overcome the problem, for example, the frequency equalization methods proposed by Steffen Trautmann, et al. are effective (see Patent Document 1 and Non-Patent Literature 1). In these methods, null carriers (subcarriers not power-transmitted) included in an OFDM signal are used to suppress a delay time on a time axis.
More specifically, for example, the receiver converts time signals into subcarrier signals for each of the subcarriers by removing the guard interval in a “GI Removal module” and performing FFT in a “DFT module”. However, in an environment in which delayed waves that exceed the guard interval arrive, the frequency signals for each of the subcarriers are not completely orthogonal to one another and cause interference to one another.
To suppress such interference and realize the frequency equalization, an equalization matrix E needs to satisfy the following Equations (1) and (2):S1,redTES1,red=D1,red−1  (1)S0,redTEWMCerr(I3×iWMS1,red)=0  (2)D1,red=S1,redTDS1,red Cerr=C−Ccycl Ccycl=iWMDWM In Equation (2), the variable S1,red represents a data signal row selection matrix; S0,red, a null carrier row selection matrix; E, a frequency equalization matrix; D, a propagation channel frequency matrix; WM, a DFT matrix; C, a propagation channel time matrix; Ccycl, a propagation channel time matrix; and I3, a unit matrix of 3×3. Moreover, the superscript −1 represents an inverse matrix; the superscript T, a complex conjugate transpose; and ×, the Kronecker product.
Therefore, in the conventional receiver, a ZF standard is applied to Equations (1) and (2) and an “E-Matrix Generator module” is made to create the frequency equalization matrix E according to the following Equation (3):E=S1,redD1,red−1S1,redT−S1,redD1,red−1W1,redW0,red+S0,redT  (3)W1,red=S1,redTWMZc,redT W0,red=S0,redTWMZc,redT In Equation (3), the variable Zc,red represents an error channel row selection matrix. Moreover, the superscript + represents an MP general inverse matrix.
The frequency equalization matrix E has an effect of removing the interference due to the delayed waves using redundancy of null carriers based on the ZF (Zero Forcing) standard. Moreover, as described above, the frequency equalization matrix E can be calculated by using the known matrices S1,red and S0,red, the propagation channel information D1,red estimated from the OFDM signal, and the error channel row selection matrix Zc,red.
Finally, an “E-Matrix Multiplier module” obtains frequency information for each of the subcarriers, the interference due to the delayed waves on which is suppressed, by multiplying a signal output from the “DFT module” with the frequency equalization matrix E.
The conventional receiver applies an MMSE (Minimum Mean Square Error) standard to create the equalization matrix E represented by Equation (4):ei,red=σui2hred,((d−1)N+1)*F1,redT·(F1,redRhhF1,redT+σr2F1,redF1,redT)−1  (4)ei=ei,redZi,red F1,red=Zi,redWM Hred=C(I3×iWMS1,red)Rhh=HredRuuHredT ei is an i-th row component of the equalization matrix E and hred,((d−1)N+1) is a row component of (d−1)N+i of Hred. Ruu represents an auto-correlation function of an input signal, Zi,red represents an extraction matrix used for extracting a non-zero element of ei, and C represents a channel matrix in a time domain.
To calculate the equalization matrix E according to the MMSE standard, it is necessary to calculate Equation (4) the number of times equal to the number of effective carriers.    Patent Document 1: International Publication No. 03/039088 Pamphlet    Non-Patent Literature 1: Steffen Trautmann and Norbert J. Fliege, “Perfect Equalization for DMT Systems Without Guard Interval”, IEEE Journal on Selected Areas in Communications, vol. 20, No. 5, June 2002